A B C D A Figure 6.67 Figure 6.66 Select Entities. … · Ch06-H6875.tex 24/11/2006 17: 48 page 301 6.3 Steady-state thermal analysis of a pipe intersection 301 A B C D ... When the

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6.3 Steady-state thermal analysis of a pipe intersection 301

A

B

C

D

Figure 6.66 Select Entities.

A

Figure 6.67 Apply Thermal Con-vection on Nodes.

A

B

Figure 6.68 Select All Nodes.

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302 Chapter 6 Application of ANSYS to thermo mechanics

A

B

C

D


A

Figure 6.70 Select All Nodes.

shown in Figure 6.69. Next, constraints at nodes located at the far edge of the tank(additional subset of nodes just selected) have to be applied. From ANSYS MainMenu select Solution → Define Loads → Apply → Thermal → Temperature →On Nodes. The frame shown in Figure 6.70 appears.

Click [A] Pick All as shown in Figure 6.70. This action brings another frameshown in Figure 6.71.

Activate both [A] All DOF and TEMP and input [B] TEMP value = 232◦C asshown in Figure 6.71. Finally, click [C] OK to apply temperature constraints onnodes at the far edge of the tank. The steps outlined above should be followed toapply constraints at nodes located at the bottom of the tank. From Utility Menuselect Select → Entities. The frame shown in Figure 6.72 appears.

From the first pull down menu select [A] Nodes, from the second pull downmenu select [B] By Location. Also, activate [C] Y coordinates button and [D] enterMin,Max = 0 (location of the bottom of the tank in Y-direction). All the four requiredsteps are shown in Figure 6.72. Next, constraints at nodes located at the bottomof the tank (additional subset of nodes selected above) have to be applied. FromANSYS Main Menu select Solution → Define Loads → Apply → Thermal →Temperature → On Nodes. The frame shown in Figure 6.70 appears. As shown in

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A

B

C

Figure 6.71 Apply Temperature to All Nodes.

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B

C

D


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Figure 6.70, click [A] Pick All in order to bring the frame shown in Figure 6.71. Asbefore, activate both [A] All DOF and TEMP and input [B] TEMP value = 232◦C.Clicking [C] OK applies temperature constraints on nodes at the bottom of the tank.

Now, it is necessary to rotate the WP to the pipe axis. From Utility Menu selectWorkPlane → Offset WP by Increments. Figure 6.73 shows the resulting frame.

A

Figure 6.73 Offset WP by Increments.

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In degrees box input [A] XY = 0 and YZ = −90 as shown. Having WP rotatedto the pipe axis, a local cylindrical coordinate system has to be defined at the originof the WP. From Utility Menu select WorkPlane → Local Coordinate Systems →Create local CS → At WP Origin. The resulting frame is shown in Figure 6.74.

A

B

Figure 6.74 Create Local CS.

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B

C

D


From the pull down menu select [A] Cylin-drical 1 and click [B] OK button to imple-ment the selection. The analysis involves nodeslocated on inner surface of the pipe. In order toinclude this subset of nodes, from Utility Menuselect Select → Entities. Figure 6.75 shows theresulting frame.

From the first pull down menu select [A]Nodes, from the second pull down menu select[B] By Location. Also, activate [C] X coor-dinates button and [D] enter Min,Max = 0.4(inside radius of the pipe). All the four requiredsteps are shown in Figure 6.75. From ANSYSMain Menu select Solution → Define Load →Apply → Thermal → Convection → On nodes.In the resulting frame (shown in Figure 6.67),press [A] Pick All and the next frame, shown inFigure 6.76, appears.

Input [A] Film coefficient = −2 and [B]Bulk temperature = 38 as shown in Figure 6.76.Pressing [C] OK button implements the selec-tions. The values inputted are taken fromTable 6.1. The final action is to select all enti-ties involved with a single command. Therefore,from Utility Menu select Select → Everything.For the loads to be applied to tank and pipesurfaces in the form of arrows from Utility Menu

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A

B

C

Figure 6.76 Apply CONV on Nodes.

select PlotCtrls → Symbols. The frame in Figure 6.77 shows the required selection:[A] Arrows.

From Utility Menu selecting Plot → Nodes results in Figure 6.78 where surfaceloads at nodes as shown as arrows.

From Utility Menu select WorkPlane → Change Active CS to → SpecifiedCoord Sys in order to activate previously defined coordinate system. The frameshown in Figure 6.79 appears.

Input [A] KCN (coordinate system number) = 0 to return to Cartesian system.Additionally from ANSYS Main Menu select Solution → Analysis Type → Sol’nControls. As a result, the frame shown in Figure 6.80 appears.

Input the following [A] Automation time stepping = On and [B] Number ofsubsteps = 50 as shown in Figure 6.80. Finally, from ANSYS Main Menu selectSolve → Current LS and in the appearing dialog box click OK button to start thesolution process.

6.3.5 Postprocessing stage

When the solution is done, the next stage is to display results in a form required toanswer questions posed by the formulation of the problem.

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A

Figure 6.77 Symbols.

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Figure 6.78 Convection surface loads displayed as arrows.

A

Figure 6.79 Change Active CS to Specified CS.

From Utility Menu select PlotCtrls → Style → Edge Options. Figure 6.81 showsthe resulting frame.

Select [A] All/Edge only and [B] press OK button to implement the selectionwhich will result in the display of the “edge” of the object only. Next, graphic controlsought to be returned to default setting. This is done by selecting from Utility MenuPlotCtrls → Symbols. The resulting frame, as shown in Figure 6.82, contains alldefault settings.

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A

B

Figure 6.80 Solution Controls.

A

B

Figure 6.81 Edge Options.

The first plot is to show temperature distribution as continuous contours. FromANSYS Main Menu select General Postproc → Plot Results → Contour Plot →Nodal Solu. The resulting frame is shown in Figure 6.83.

Select [A] Temperature and press [B] OK button as shown in Figure 6.83. Theresulting temperature map is shown in Figure 6.84.

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Figure 6.82 Symbols.

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A

B

Figure 6.83 Contour Nodal Solution Data.

Figure 6.84 Temperature map on inner surfaces of the tank and the pipe.

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The next display of results concerns thermal flux at the intersection betweenthe tank and the pipe. From ANSYS Main Menu select General Postproc → PlotResults → Vector Plot → Predefined. The resulting frame is shown in Figure 6.85.

A

B

C

Figure 6.85 Vector Plot Selection.

In Figure 6.85, select [A] Thermal flux TF and [B] Raster Mode. Pressing [C] OKbutton implements selections and produces thermal flux as vectors. This is shown inFigure 6.86.

6.4 Heat dissipation through ribbed surface

6.4.1 Problem description

Ribbed or developed surfaces, also called fins, are frequently used to dissipate heat.There are many examples of their use in practical engineering applications such ascomputers, electronic systems, radiators, just to mention a few of them.

Figure 6.87 shows a typical configuration and geometry of a fin made of aluminumwith thermal conductivity coefficient k = 170 W/m K.

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6.4 Heat dissipation through ribbed surface 313

Figure 6.86 Distribution of thermal flux vectors at the intersection between the tank and the pipe.

330

20 20 20

10

100

85

85

40 25 50

Figure 6.87 Cross-section of the fin.

The bottom surface of the fin is exposed to a constant heat flux of q = 1000 W/m.Air flows over the developed surface keeping the surrounding temperature at293 K. Heat transfer coefficient between the fin and the surrounding atmosphereis h = 40 W/m2 K.

Determine the temperature distribution within the developed surface.

6.4.2 Construction of the model

From ANSYS Main Menu select Preferences to call up a frame shown in Figure 6.88.

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A

Figure 6.88 Preferences: Thermal.

Because the problem to be solved is asking for temperature distribution, there-fore [A] Thermal is selected as indicated in the figure. Next, from ANSYS MainMenu select Preprocessor → Element Type → Add/Edit/Delete. The frame shownin Figure 6.89 appears.

A

Figure 6.89 Define element type.

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Click [A] Add button to call up another frame shown in Figure 6.90.

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B

Figure 6.90 Library of Element Types.

In Figure 6.90, the following selections are made: [A] Thermal Mass → Solidand [B] Tet 10node 87. From ANSYS Main Menu select Preprocessor → MaterialProps → Material Models. Figure 6.91 shows the resulting frame.

A

Figure 6.91 Define Material Model Behavior.

From the right-hand column select [A] Thermal → Conductivity → Isotropic.In response to this selection another frame, shown in Figure 6.92, appears.

Thermal conductivity [A] KXX = 170 W/m K is entered and [B] OK buttonclicked to implement the entry as shown in the figure.

The model of the developed area will be constructed using primitives and it isuseful to have them numbered. Thus, from ANSYS Utility Menu select PlotCtrls →Numbering and check [A] the box area numbers on as shown in Figure 6.93.

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A

B

Figure 6.92 Conductivity coefficient.

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Figure 6.93 Numbering Controls.

From ANSYS Main Menu select Preprocessor → Modelling → Create → Areas→ Rectangle → By Dimensions. Figure 6.94 shows the resulting frame.

Input [A] X1 = −165; [B] X2 = 165; [C] Y1 = 0; [D] Y2 = 100 to create rectan-gular area (A1) within which the fin will be comprised. Next create two rectangles

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A

C

B

D

Figure 6.94 Create Rectangle by Dimensions.

at left and right upper corner to be cut off from the main rectangle. From ANSYSMain Menu select Preprocessor → Modelling → Create → Areas → Rectangle →By Dimensions. Figure 6.95 shows the resulting frame.

A

C

B

D

Figure 6.95 Rectangle with specified dimensions.

Figure 6.95 shows inputs to create rectangle (A2) at the left-hand upper cornerof the main rectangle (A1). They are: [A] X1 = −165; [B] X2 = −105; [C] Y1 = 85;[D] Y2 = 100. In order to create right-hand upper corner rectangles (A3) repeat theabove procedure and input: [A] X1 = 105; [B] X2 = 165; [C] Y1 = 85; [D] Y2 = 100.Now, areas A2 and A3 have to be subtracted from area A1. From ANSYS Main Menuselect Preprocessor → Modelling → Operate → Booleans → Subtract → Areas.Figure 6.96 shows the resulting frame.

First, select area A1 (large rectangle) to be subtracted from and [A] click OKbutton. Next, select two smaller rectangles A2 and A3 and click [A] OK button. Anew area A4 is created with two upper corners cut off. Proceeding in the same way,areas should be cut off from the main rectangle in order to create the fin shown inFigure 6.87.

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A

Figure 6.96 Subtract Areas.

From ANSYS Main Menu select Prepro-cessor → Modelling → Create → Areas →Rectangle → By Dimensions. Figure 6.97shows the frame in which appropriate inputshould be made.

In order to create area A1 input: [A]X1 = −145; [B] X2 = −125; [C] Y1 = 40; [D]Y2 = 85. In order to create area A2 input:[A] X1 = 125; [B] X2 = 145; [C] Y1 = 40; [D]Y2 = 85. In order to create area A3 input: [A]X1 = −105; [B] X2 = −95; [C] Y1 = 25; [D]Y2 = 100. In order to create area A5 input:[A] X1 = 95; [B] X2 = 105; [C] Y1 = 25; [D]Y2 = 100.

From ANSYS Main Menu select Prepro-cessor → Modelling → Operate → Booleans→ Subtract → Areas. The frame shown inFigure 6.96 appears. Select first area A4 (largerectangle) and click [A] OK button. Next, selectareas A1, A2, A3, and A5 and click [A] OKbutton. Area A6 with appropriate cut-outs iscreated. It is shown in Figure 6.98.

In order to finish construction of the fin’smodel use the frame shown in Figure 6.97 andmake the following inputs: [A] X1 = −85; [B]X2 = −75; [C] Y1 = 25; [D] Y2 = 100. AreaA1 is created. Next input: [A] X1 = −65; [B]

A

C

B

D

Figure 6.97 Create rectangle by four coordinates.

X2 = −55; [C] Y1 = 25; [D] Y2 = 100 to create area A2. Next input: [A] X1 = −45;[B] X2 = −35; [C] Y1 = 25; [D] Y2 = 100 to create area A3. Appropriate inputsshould be made to create areas, to be cut out later, on the right-hand side of the fin.Thus inputs: [A] X1 = 85; [B] X2 = 75; [C] Y1 = 25; [D] Y2 = 100 create area A4.Inputs: [A] X1 = 65; [B] X2 = 55; [C] Y1 = 25; [D] Y2 = 100 create area A5. Inputs

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Figure 6.98 Image of the fin after some areas were subtracted.

[A] X1 = 45; [B] X2 = 35; [C] Y1 = 25; [D] Y2 = 100 create area A7. Next, fromANSYS Main Menu select Preprocessor → Modelling → Operate → Booleans →Subtract → Areas. The frame shown in Figure 6.96 appears. Select first area A6 andclick [A] OK button. Then, select areas A1, A2, A3, A4, A5, and A7. Clicking [A]OK button implements the command and a new area A8 with appropriate cut-outs iscreated. In order to finalize the construction of the model make the following inputsto the frame shown in Figure 6.97 to create area A1: [A] X1 = −25; [B] X2 = −15; [C]Y1 = 50; [D] Y2 = 100. Inputs: [A] X1 = −5; [B] X2 = 5; [C] Y1 = 50; [D] Y2 = 100create area A2. Finally input [A] X1 = 15; [B] X2 = 25; [C] Y1 = 50; [D] Y2 = 100to create area A3. Again from ANSYS Main Menu select Preprocessor → Modelling→ Operate → Booleans → Subtract → Areas. The frame shown in Figure 6.96appears. Select first area A8 and click [A] OK button. Next, select areas A1, A2, andA3. Clicking [A] OK button produces area A4 shown in Figure 6.99. Figure 6.99shows the final shape of the fin with dimensions as specified in Figure 6.87. It is,however, a 2D model. The width of the fin is 100 mm and this dimension can be usedto create 3D model.

Figure 6.99 Two-dimensional image of the fin.

From ANSYS Main Menu select Preprocessor → Modelling → Operate →Extrude → Areas → Along Normal. Select Area 4 (to be extruded in the directionnormal to the screen, i.e., z-axis) and click OK button. In response, the frame shownin Figure 6.100 appears.

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A

B

Figure 6.100 Extrude area.

Input [A] Length of extrusion = 100 mm and [B] click OK button. The 3D modelof the fin is created as shown in Figure 6.101.

Figure 6.101 Three-dimensional (isometric) view of the fin.

The fin is shown in isometric view without area numbers. In order to deselectnumbering of areas refer to Figure 6.93 in which box Area numbers should bechecked off.

From ANSYS Main Menu select Preprocessor → Meshing → MeshAttributes → Picked Volumes. The frame shown in Figure 6.102 is created.

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A

Figure 6.102 Volume Attributes.

Select [A] Pick All and the next frame, shown in Figure 6.103, appears.Material Number 1 and element type SOLID87 are as specified at the beginning

of the analysis and in order to accept that click [A] OK button.Now meshing of the fin can be carried out. From ANSYS Main Menu select

Preprocessor → Meshing → Mesh → Volumes → Free. The frame shown inFigure 6.104 appears.

Select [A] Pick All option, as shown in Figure 6.104, to mesh the fin. Figure 6.105shows the meshed fin.

6.4.3 Solution

Prior to running solution stage boundary conditions have to be properly applied. Inthe case considered here the boundary conditions are expressed by the heat transfercoefficient which is a quantitative measure of how efficiently heat is transferred fromfin surface to the surrounding air.

From ANSYS Main Menu select Solution → Define Loads → Apply →Thermal → Convection → On Areas. Figure 6.106 shows the resulting frame.

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A

Figure 6.103 Volume attributes with specified material and element type.

A

Figure 6.104 Mesh Volumes.

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Figure 6.105 View of the fin with mesh network.

A

Figure 6.106 Apply boundary conditions tothe fin areas.

Select all areas of the fin except the bot-tom area and click [A] OK button. The framecreated as a result of that action is shown inFigure 6.107.

Input [A] Film coefficient = 40 W/m2 K;[B] Bulk temperature = 293 K and click [C]OK button. Next a heat flux of intensity1000 W/m has to be applied to the base of thefin. Therefore, from ANSYS Main Menu selectSolution → Define Loads → Apply → Ther-mal → Heat Flux → On Areas. The resultingframe is shown in Figure 6.108.

Select the bottom surface (base) of the finand click [A] OK button. A new frame appears(see Figure 6.109) and the input made is asfollows: [A] Load HFLUX value = 1000 W/m.Clicking [B] OK button implements the input.

All required preparations have been madeand the model is ready for solution. FromANSYS Main Menu select Solution → Solve→ Current LS. Two frames appear. One givesa summary of solution options. After checkingcorrectness of the options, it should be closedusing the menu at the top of the frame. Theother frame is shown in Figure 6.110.

Clicking [A] OK button starts the solutionprocess.

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A

B

C

Figure 6.107 Apply heat transfer coefficient and surrounding temperature.

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Figure 6.108 Apply heat flux on the fin base.

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A

B

Figure 6.109 Apply heat flux value on the fin base.

A

Figure 6.110 Solve the problem.

6.4.4 Postprocessing

Successful solution is signaled by the message “solution is done.” The postprocess-ing phase can be initiated now in order to view the results. The problem asks fortemperature distribution within the developed area.

From ANSYS Main Menu select General Postproc → Plot Results → ContourPlot → Nodal Solution. The frame shown in Figure 6.111 appears.

Select [A] Thermal Flux; [B] thermal flux vector sum and click [C] OK toproduce the graph shown in Figure 6.112.

In order to observe how the temperature changes from the base surface to the topsurface of the fin a path along which the variations take place has to be determined.

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A

B

C


From ANSYS Main Menu select General Postproc → Path Operations → DefinePath → On Working Plane. The resulting frame is shown in Figure 6.113.

By activating [A] Arbitrary path button and clicking [B] OK button anotherframe, shown in Figure 6.114, is produced.

Two points should be picked that is on the bottom line at the middle of the finand, moving vertically upward, on the top line of the fin. After that [A] OK buttonshould be clicked. A new frame appears as shown in Figure 6.115.

In the box [A] Define Path Name, write AB and click [B] OK button.From ANSYS Main Menu select General Postproc → Path Operations → Map

onto Path. The frame shown in Figure 6.116 appears.Select [A] Flux & gradient; [B] TGSUM and click [C] OK button. Next, from

ANSYS Main Menu select General Postproc → Path Operations → Plot Path Item→ On Graph. Figure 6.117 shows the resulting frame.

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Figure 6.112 Heat flux distribution.

A

B

Figure 6.113 Arbitrary path selection.

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Figure 6.114 Arbitrary path on working plane.

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B

Figure 6.115 Path name definition.

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B

C

Figure 6.116 Map results on the path.

A

B

Figure 6.117 Selection of items to be plotted.

Select [A] TGSUM and click [B] OK button to obtain a graph shown inFigure 6.118.

The graph shows temperature gradient variation as a function of distance fromthe base of the fin.

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Figure 6.118 Temperature gradient plot as a function of distance from the fin base.

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7C h a p t e r

Application ofANSYS to ContactBetween Machine

Elements

Chapter outline

7.1 General characteristics of contact problems 3317.2 Example problems 332

7.1 General characteristics of contactproblems

In almost every mechanical device, constituent components are in either rollingor sliding contact. In most cases, contacting surfaces are non-conforming so that

the area through which the load is transmitted is very small, even after some surfacedeformation, and the pressures and local stresses are very high. Unless purposefullydesigned for the load and life expected of it, the component may fail by early generalwear or by local fatigue failure. The magnitude of the damage is a function of thematerials and the intensity of the applied load as well as the surface finish, lubrication,and relative motion.

The intensity of the load can usually be determined from equations, which arefunctions of the geometry of the contacting surfaces, essentially the radii of curvature,and the elastic constants of the materials. Large radii and smaller modules of elasticitygive larger contact areas and lower pressures.

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332 Chapter 7 Application of ANSYS to contact between machine elements

A contact is said to be conforming (concave) if the surfaces of the two elements fitexactly or even closely together without deformation. Journal bearings are an exampleof concave contact. Elements that have dissimilar profiles are considered to be non-conforming (convex). When brought into contact without deformation they touchfirst at a point, hence point contact or along line, line contact. In a ball bearing, the ballmakes point contact with the inner and outer races, whereas in a roller bearing theroller makes line contact with both the races. Line contact arises when the profilesof the elements are conforming in one direction and non-conforming in the perpen-dicular direction. The contact area between convex elements is very small comparedto the overall dimensions of the elements themselves. Therefore, the stresses are highand concentrated in the region close to the contact zone and are not substantiallyinfluenced by the shape of the elements at a distance from the contact area.

Contact problem analyses are based on the Hertz theory, which is an approxi-mation on two counts. First, the geometry of general curved surfaces is described byquadratic terms only and second, the two bodies, at least one of which must havea curved surface, are taken to deform as though they were elastic half-spaces. Theaccuracy of Hertz theory is in doubt if the ratio a/R (a is the radius of the contactarea and R is the radius of curvature of contacting elements) becomes too large. Withmetallic elements this restriction is ensured by the small strains at which the elasticlimit is reached. However, a different situation arises with compliant elastic solidslike rubber. A different problem is encountered with conforming (concave) surfacesin contact, for example, a pin in a closely fitting hole or by a ball and socket joint.Here, the arc of contact may be large compared with the radius of the hole or socketwithout incurring large strains.

Modern developments in computing have stimulated research into numericalmethods to solve problems in which the contact geometry cannot be described ade-quately by the quadratic expressions used originally by Hertz. The contact of wornwheels and rails or the contact of conforming gear teeth with Novikov profile are thetypical examples. In the numerical methods, contact area is subdivided into a gridand the pressure distribution represented by discrete boundary elements acting on theelemental areas of the grid. Usually, elements of uniform pressure are employed, butoverlapping triangular elements offer some advantages. They sum to approximatelylinear pressure distribution and the fact that the pressure falls to zero at the edge ofthe contact ensures that the surfaces do not interfere outside the contact area. Thethree-dimensional (3D) equivalent of overlapping triangular elements is overlappinghexagonal pyramids on an equilateral triangular grid.

An authoritative treatment of contact problems can be found in the monographby Johnson [1].

7.2 Example problems

7.2.1 Pin-in-hole interference fit

7.2.1.1 PROBLEM DESCRIPTION

One end of a steel pin is rigidly fixed to the solid plate while its other end is forcefitted to the steel arm. The configuration is shown in Figure 7.1.

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7.2 Example problems 333

Figure 7.1 Illustration of the problem.

This is a 3D analysis but because of the inherent symmetry of the model, analysiswill be carried out for a quarter-symmetry model only. There are two objectives ofthe analysis. The first is to observe the force fit stresses of the pin, which is pushedinto the arm’s hole with geometric interference. The second is to find out stresses,contact pressures, and reaction forces due to a torque applied to the arm (force actingat the arm’s end) and causing rotation of the arm. Stresses resulting from shearing ofthe pin and bending of the pin will be neglected purposefully.

The dimensions of the model are as follows: pin radius = 1 cm, pin length = 3 cm;arm width = 4 cm, arm length = 12 cm, arm thickness = 2 cm; and hole in the arm:radius = 0.99 cm, depth = 2 cm (through thickness hole).

Both the elements are made of steel with Young’s modulus = 2.1 × 109 N/m2,Poisson’s ratio = 0.3 and are assumed to be elastic.

7.2.1.2 CONSTRUCTION OF THE MODEL

In order to analyze the contact between the pin and the hole, a quarter-symmetrymodel is appropriate. It is shown in Figure 7.2.

In order to create a model shown in Figure 7.2, two 3D primitives are used,namely block and cylinder. The model is constructed using graphical user interface(GUI) only. It is convenient for carrying out Boolean operations on volumes to have

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Figure 7.2 A quarter-symmetry model.

them numbered. This can be done by selecting from Utility Menu → PlotCtrls →Numbering and checking appropriate box to activate VOLU (volume numbers)option.

From ANSYS Main Menu select Preprocessor → Modelling → Create →Volumes → Block → By Dimensions. In response, a frame shown in Figure 7.3appears.

A

Figure 7.3 Create Block by Dimensions.

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A

Figure 7.4 Create Cylinder by Dimensions.

A

Figure 7.5 Overlap Volumes.

It can be seen from Figure 7.3 that appropriateX, Y, and Z coordinates were entered. Clicking [A]OK button implements the entries. A block withlength 5 cm, width 5 cm, and thickness 2 cm (vol.1) is created.

Next, from ANSYS Main Menu select Prepro-cessor → Modelling → Create → Volumes →Cylinder → By Dimensions. In response, a frameshown in Figure 7.4 appears.

The inputs are shown in Figure 7.4. Clicking[A] OK button implements the entries and createsa solid cylinder sector with radius 1 cm, length5.5 cm, starting angle 270◦, and ending angle 360◦(vol. 2).

From ANSYS Main Menu select Preprocessor→ Modelling → Operate → Booleans → Over-lap → Volumes. The frame shown in Figure 7.5appears.

Block (vol. 1) and cylinder (vol. 2) should bepicked and [A] OK button pressed. As a result ofthat block and cylinder are overlapped.

From ANSYS Main Menu select Preprocessor→ Modelling → Create →Volumes → Block →By Dimensions. The frame shown in Figure 7.6appears.

Coordinates X,Y, and Z were used as shown in Figure 7.6. Clicking [A] OK buttonimplements the entries and, as a result, a block volume was created with length 10 cm,width 2 cm, and thickness 2 cm (vol. 2).

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A


From ANSYS Main Menu select Preprocessor → Modelling → Create →Volumes → Cylinder → By Dimensions. The frame shown in Figure 7.7 appears.

A


Input data entered are shown in Figure 7.7. Clicking [A] OK button implementsthe entries. As a result solid cylinder sector with radius 0.99 cm, length 2 cm, startingangle 270◦, and ending angle 360◦ (vol. 2) is produced. Next, volume 2 must besubtracted from volume 1 to produce a hole in the arm with the radius of 0.99 cm,which is smaller than the radius of the pin. In this way, an interference fit betweenthe pin and the arm is created.

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A

Figure 7.8 Subtract Volumes.

From ANSYS Main Menu select Preproces-sor → Modelling → Operate → Booleans →Subtract → Volumes. The frame shown inFigure 7.8 appears.

Volume 2 (short solid cylinder sector withradius 0.99 cm) is subtracted from volume 1 (thearm) by picking them in turn and pressing [A]OK button. As a result volume 6 is created.

From ANSYS Main Menu select Mod-elling → Move/Modify → Volumes. Then pickvolume 6 (the arm), which is to be moved, andclick OK. The frame shown in Figure 7.9 appears.

In order to move the arm (vol. 6) in requiredposition, coordinates shown in Figure 7.9 shouldbe used. Clicking [A] OK button implements themove action.

From Utility Menu select Plot → Replot toview the arm positioned in required location.Finally from Utility Menu select PlotCtrls →View Settings → Viewing Direction. The frameshown in Figure 7.10 appears.

By selecting coordinates X, Y, and Z as shownin Figure 7.10 and activating [A] Plot → Replotcommand (Utility Menu), a quarter-symmetrymodel, as shown in Figure 7.2, is finally created.

A

Figure 7.9 Move Volumes.

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A

Figure 7.10 Viewing Direction.

7.2.1.3 MATERIAL PROPERTIES AND ELEMENT TYPE

The next step in the analysis is to define the properties of the material used to makethe pin and the arm.

From ANSYS Main Menu select Preferences. The frame shown in Figure 7.11 isproduced.

A

Figure 7.11 Preferences.

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From the Preferences list [A] Structural option was selected as shown inFigure 7.11.

From ANSYS Main Menu select Preprocessor → Material Props → MaterialModels.

Double click Structural → Linear → Elastic → Isotropic. The frame shown inFigure 7.12 appears.

A

B

C

Figure 7.12 Material Properties.

Enter [A] EX = 2.1 × 109 for Young’s modulus and [B] PRXY = 0.3 for Poisson’sratio. Then click [C] OK and afterward Material → Exit.

After defining the properties of the material, the next step is to select the elementtype appropriate for the analysis.

From ANSYS Main Menu select Preprocessor → Element Type → Add/Edit/Delete. The frame shown in Figure 7.13 appears.

Click [A] Add in order to pull down another frame as shown in Figure 7.14.In the left column click [A] Structural Solid and in the right column click [B]

Brick 8node 185. After that click [C] OK and [B] Close in the frame shown inFigure 7.13. This completes the element type selection.

7.2.1.4 MESHING

From ANSYS Main Menu select Preprocessor → Meshing → MeshTool.The frame shown in Figure 7.15 appears.There are a number of options available. First step is to go to [A] Size Con-

trol → Lines option and click [B] Set button. This opens another frame (shown inFigure 7.16) prompting to pick lines on which element size is going to be controlled.

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A

B

Figure 7.13 Element Types.

A

C

B


Pick the horizontal and vertical lines on the front edge of the pin and click [A] OK.The frame shown in Figure 7.17 appears. In the box, [A] No. of element divisionstype 3 and change selection [B] SIZE, NDIV can be changed to No. by checking thebox and, finally, click [C] OK.

Using MeshTool frame again (as shown in Figure 7.18) click button [A] Set in theSize Controls → Lines option and pick the curved line on the front of the arm. Click

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A

B

Figure 7.15 MeshTool options.

A

Figure 7.16 Element Size onPicked Lines.

OK afterward. The frame shown in Figure 7.17 appears. In the box No. of elementdivisions type 4 and press [C] OK button.

In the frame MeshTool (see Figure 7.18) pull down [B] Volumes in theoption Mesh.

Check [C] Hex/Wedge and [D] Sweep options. This is shown in Figure 7.18.Pressing [E] Sweep button brings another frame asking to pick the pin and the

arm volumes (see Figure 7.19).

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A

B

C

Figure 7.17 Element Sizes on Picked Lines.

Pressing [A] OK button initiates meshing process. The model after meshing lookslike the image in Figure 7.20.

Pressing [F] Close button on MeshTool frame (see Figure 7.18) ends meshgeneration stage.

After meshing is completed, it is usually necessary to smooth element edges inorder to improve graphic display. It can be accomplished using PlotCtrls facility inthe Utility Menu.

From Utility Menu select PlotCtrls → Style → Size and Shape. The frame shownin Figure 7.21 appears.

From option [A] Facets/element edge select 2 facets/edge, which is shown inFigure 7.21.

7.2.1.5 CREATION OF CONTACT PAIR

In solving the problem of contact between two elements, it is necessary to createcontact pair. Contact Wizard is the facility offered by ANSYS.

From ANSYS Main Menu select Preprocessor → Modelling → Create →Contact Pair. As a result of this selection, a frame shown in Figure 7.22 appears.

Location of [A] Contact Wizard button is in the upper left-hand corner of theframe. By clicking on this button a new frame (shown in Figure 7.23) is produced.

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A

B

C

D

E

F

Figure 7.18 Checked Hex and Sweepoptions.

A

Figure 7.19 Volume Sweeping.

In the frame shown in Figure 7.23, select [A] Areas, [B] Flexible, and press thebutton [C] Pick Target. As a result of this selection, the frame shown in Figure 7.24is produced.

The target area is the surface of pinhole in the arm and it should be picked and[A] OK button pressed. In Contact Wizard frame (see Figure 7.23) press [D] Nextbutton (which should be highlighted when the target area is picked) to obtain anotherframe as shown in Figure 7.25.

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Figure 7.20 Model after meshing process.

A

Figure 7.21 Size and Shape control of element edges.

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A

Figure 7.22 Contact Manager.

A B

D

C

Figure 7.23 Contact Wizard.

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A

Figure 7.24 Select Areas for Target.

A

Figure 7.25 Select Areas for Contact.

Figure 7.26 Pin contact area.

Surface area of the pin should be pickedas the area for contact. When it is done andthe [A] OK button pressed, Contact Wizardframe appears (see Figure 7.23). Pressing Next[D] button produces a frame in which MaterialID = 1, Coefficient of friction = 0.2 shouldbe selected. Also, Include Initial penetrationoption should be checked. Next, Optional set-tings button should be pressed in order tofurther refine contact parameters. In the newframe, Normal penalty stiffness = 0.1 shouldbe selected. Also, Friction tab located in thetop of the frame menu should be activated and

Stiffness matrix = Unsymmetric should be selected. Afterward, pressing the buttonOK and next Create results in the image shown in Figure 7.26.

Also, Contact Wizard frame appears in the form shown in Figure 7.27.The message is that the contact pair has been created. Pressing [A] Finish button

closes the Contact Wizard tool.Contact Manager frame appears again with the information pertinent to the

problem considered. It is shown in Figure 7.28.

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A

Figure 7.27 Contact Wizard final message.

Figure 7.28 Contact Manager summary information.

7.2.1.6 SOLUTION

In the solution stage, solution criteria have to be specified first. As a first step in thatprocess, symmetry constraints are applied on the quarter-symmetry model.

From ANSYS Main Menu select, Solution → Define Loads → Apply → Struc-tural → Displacement → Symmetry BC → On Areas. The frame shown inFigure 7.29 appears.

Four areas which were created when the full configuration model was sectionedto produce quarter-symmetry model should be picked as shown in Figure 7.30. Whenthat is done, click [A] OK button in the frame shown in Figure 7.29.

The next step is to apply boundary constraints on the block of which the pin isan integral part.

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A

Figure 7.29 Apply SYMM on Areas.

Figure 7.30 Selected areas on which symmetry constraints are applied.

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A

B

Figure 7.31 Apply U,ROT on Areas.

From ANSYS Main Menu select Solution → Define Loads → Apply → Struc-tural → Displacement → On Areas.

Backside of the block should be picked and then OK button pressed. The frameshown in Figure 7.31 appears.

All degrees of freedom [A] All DOF should be constrained with the displacementvalue equal to zero (see Figure 7.31). Clicking [B] OK button applies the constraints.

Because the original problem formulation asks for stress analysis when the arm ispulled out of the pin, the analysis involves a large displacement effects. The first typeof load results from the interference fit between the pin and the arm.

From ANSYS Main Menu select Solution → Analysis Type → Sol’n Controls.The frame shown in Figure 7.32 appears. In the pull down menu select [A] LargeDisplacement Static. Further selected options should be [B] Time at end of loadstep = 100; [C] Automatic time stepping (pull down menu) = Off; and [D] Numberof substeps = 1. All specified selections are shown in Figure 7.32. Pressing [E] OKbutton applies the settings and closes the frame.

The next action is to solve for the first type of load, i.e., interference fit.From ANSYS Main Menu select Solution → Solve → Current LS. A frame show-

ing review of information pertaining to the planned solution action appears. Afterchecking that everything is correct, select File → Close to close that frame. PressingOK button starts the solution. When the solution is completed, press Close button.

In order to return to the previous image of the model, select Utility Menu →Plot → Replot.

The second type of load is created when the arm is pulled out of the pin. A numberof actions have to be taken in order to prepare the model for solution. First action isto apply a displacement along Z-axis equal to 2 cm (thickness of the arm) to all nodeson the front of the pin in order to observe this effect.

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A

B

C

D

E


A

B

C

D


A

Figure 7.34 Apply U,ROT on Nodes.

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From Utility Menu → Select → Entities. The frame shown in Figure 7.33appears.

In this frame the following selections should be made: [A] Nodes (from pull downmenu); [B] By Location (pull down menu); [C] Z coordinates (to be checked); Min,Max = 4,5. Pressing [D] OK implements the selections made.

Next, degrees of freedom in the Z-direction should be constrained with thedisplacement value of 2 (thickness of the arm).

From ANSYS Main Menu select Solution → Define Loads → Apply → Struc-tural → Displacement → On Nodes. In response, a frame shown in Figure 7.34appears.

By pressing [A] Pick All button, a frame shown in Figure 7.35 is called up.As shown in Figure 7.35, [A] DOF to be constrained = UZ and the [B]

Displacement value = 2. Pressing [C] OK button applies selected constraints.

A

B

C

Figure 7.35 Apply U,ROT on Nodes.

Options for the analysis of pull-out operation have to be defined now.From ANSYS Main Menu select Solution → Analysis Type → Sol’n Controls.

The frame shown in Figure 7.36 appears in response.As shown in Figure 7.36, the following selections defining solution controls were

made: [A] Time at end of load step = 200; [B] Automatic time stepping (pull downmenu) = On; [C] Number of substeps = 100; [D] Max no. of substeps = 10,000;[E] Min no. of substeps = 10; and Frequency (pull down menu) = Write every N thsubstep, where N = −10. Pressing [F] OK button applied selected controls.

Now the model is ready to be solved for the load resulting from pulling thearm out.

From ANSYS Main Menu select Solution → Solve → Current LS. A framegiving summary information pertinent to the solution appears. After reviewing theinformation select File → Close to close the frame. After that, pressing OK buttonstarts the solution. When the solution is done, press Close button.

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A

B

C

E

D

F


During solution process warning messages could appear. In order to make surethat the solution is done, it is practical to issue the command in the input box: /NERR,100, 100, 0FF. This ensures that ANSYS program does not abort if it encounters aconsiderable number of errors.

7.2.1.7 POSTPROCESSING

Postprocessing stage is used to display solution results in a variety of forms.The first thing to do is to expand the quarter-symmetry model into full

configuration model.From Utility Menu select PlotCtrls → Style → Symmetry Expansion →

Periodic/ Cyclic Symmetry. Figure 7.37 shows the resulting frame.Click [A] ¼ Dihedral Sym button as shown in Figure 7.37 and press [B] OK.From Utility Menu select Plot → Elements. An image of the full configuration

model appears as shown in Figure 7.38.The first set of results to observe in the postprocessing stage is to look at the state

of stress due to interference fit between the pin and the hole in the arm.From ANSYS Main Menu select General Postproc → Read Results → By Load

Step. The frame shown in Figure 7.39 is produced.The selection [A] Load step number = 1 is shown in Figure 7.39. By clicking [B]

OK button the selection is implemented.

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A

B

Figure 7.37 Periodic/Cyclic Symmetry Expansion.

Figure 7.38 Full model with mesh of elements and applied constraints.

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A

B

Figure 7.39 Read Results by Load Step Number.

From ANSYS Main Menu select General Postproc → Plot Results → ContourPlot → Nodal Solu. In the resulting frame, see Figure 7.40, the following selections

A

B

C


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are made: [A] Item to be contoured = Stress and [B] Item to be contoured = vonMises (SEQV). Pressing [C] OK button implements selections.

Contour plot of von Mises stress (nodal solution) is shown in Figure 7.41.

Figure 7.41 Contour plot of nodal solution (von Mises stress).

Figure 7.41 shows stress contour plot for the assembly of the pin in the hole. Inorder to observe contact pressure on the pin resulting from the interference fit, it isrequired to read results by time/frequency.

From ANSYS Main Menu select General Postproc → Read Results → ByTime/Freq.

In the resulting frame, shown in Figure 7.42, the selection to be made is: [A] Valueof time or freq. = 120. Pressing [B] OK implements the selection.

From Utility Menu choose, Select → Entities. The frame shown in Figure 7.43appears.

In the frame shown in Figure 7.43, the following selections are made: [A] Elements(from pull down menu); [B] By Elem Name (from pull down menu); and [C] ElementName = 174. The element with the number 174 was introduced automatically duringthe process of creation of contact pairs described earlier. It is listed in the Prepro-cessor → Element Type → Add/Edit/Delete option. Selections are implemented bypressing [D] OK button.

From Utility Menu select Plot → Elements. Image of the pin with surfaceelements is produced (see Figure 7.44).

From ANSYS Main Menu select General Postproc → Plot Results → ContourPlot → Nodal Solu. The frame shown in Figure 7.45 appears.

In the frame shown in Figure 7.45, the following selections are made: [A] Contactand [B] Pressure. These are items to be contoured. Pressing [C] OK implementsselections made. Figure 7.46 shows image of the pin with pressure contours.

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A

B

Figure 7.42 Read Results by Time or Frequency.

A

B

C

D


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Figure 7.44 Pin with surface elements.

AB

C


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Figure 7.46 Contact pressure contours on surface of the pin.

The last action to be taken is to observe state of stress resulting from pulling outof the arm from the pin.

From Utility Menu choose Select → Everything. Next, from ANSYS Main Menuselect General Postproc → Read Results → By Load Step. The frame shown inFigure 7.47 appears.

A

B


As shown in Figure 7.47, [A] Load step number = 2 was selected. Pressing [B]OK implements the selection.

From ANSYS Main Menu select General Postproc → Plot Results → ContourPlot → Nodal Solu. In appearing frame (see Figure 7.40), the following are selected

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as items to be contoured: [A] Stress and [B] von Mises (SEQV). Pressing [C] OKimplements selections made. Figure 7.48 shows stress contours on the pin resultingfrom pulling out the arm.

Figure 7.48 Pull-out stress contours on the pin.

7.2.2 Concave contact between cylinder and two blocks


Configuration of the contact between cylinder and two blocks is shown in Figure 7.49.This is a typical contact problem, which in engineering applications is represented

by a cylindrical rolling contact bearing. Also, the characteristic feature of the contactis that, nominally, surface contact takes place between elements. In reality, this is neverthe case due to surface roughness and unavoidable machining errors and dimensionaltolerance. There is no geometrical interference when the cylinder and two blocks areassembled.

This is a 3D analysis and advantage could be taken of the inherent symmetry ofthe model. Therefore, the analysis will be carried out on a half-symmetry model only.The objective of the analysis is to observe the stresses in the cylinder when the initialgap between two blocks is decreased by 0.05 cm.

The dimensions of the model are as follows: cylinder radius = 0.5 cm;cylinder length = 1 cm; block length = 2 cm; block width = 1 cm; and blockthickness = 0.75 cm. Both blocks are geometrically identical. All elements are made ofsteel with Young’s modulus = 2.1 × 109 N/m2, Poisson’s ratio = 0.3 and are assumedelastic. Friction coefficient at the interface between cylinder and the block is 0.2.

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Figure 7.49 Configuration of the contact between cylinder and two blocks.

7.2.2.2 MODEL CONSTRUCTION

For the intended analysis a half-symmetry model is appropriate. It is shown inFigure 7.50.

In order to create a model shown in Figure 7.50, the use of two 3D primitives,namely block and cylinder, is made. The model is constructed using GUI facilities only.When carrying out Boolean operations on volumes it is quite convenient to have themnumbered. This is done by selecting from the Utility Menu → PlotCtrls → Num-bering and checking appropriate box to activate VOLU (volume numbers) option.

From ANSYS Main Menu select, Preprocessor → Modelling → Create → Vol-umes → Block → By Dimensions. In response, a frame shown in Figure 7.51 appears.

It can be seen from Figure 7.51 that appropriate X, Y, and Z coordinates wereentered to create a block (vol. 1) with the length 2 cm ([A] X1 = −1; X2 = 1), width1 cm ([B] Z1 = 0; Z2 = 1), and thickness 0.75 cm ([C] Y1 = −0.25; Y2 = −1). Next,from ANSYS Main Menu select Preprocessor → Modelling → Create → Vol-umes → Cylinder → By Dimensions. In response, a frame shown in Figure 7.52appears.

The input into the frame, shown in Figure 7.52, created a solid cylinder sectorwith the [A] radius 0.5 cm, [B] length 1 cm, [C] starting angle 180◦, and [D] endingangle 360◦ (vol. 2).

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Figure 7.50 A half-symmetry model.

A

C

B


From ANSYS Main Menu select Preprocessor → Modelling → Operate →Booleans → Overlap → Volumes. The frame shown in Figure 7.53 appears.

Block (vol. 1) and cylinder (vol. 2) should be picked and [A] OK button pressed.As a result of that, block and cylinder are overlapped and three volumes created, i.e.,volume 5 (block), volume 3 (section of the cylinder within the block), and volume 4(remaining of the cylinder after a section of it has been subtracted).

From ANSYS Main Menu select Modelling → Delete → Volume and Below.The frame shown in Figure 7.54 appears.

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A

B

C

D


A

Figure 7.53 Overlap Volumes.

A

Figure 7.54 Delete Volume &Below.

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Picking volume 4 and clicking [A] OK deletes it. The same operation should berepeated to deleted volume 3. As a result of that a block should be produced. Frontview of the block is shown in Figure 7.55.

Figure 7.55 Block with a cylindrical cut-out.

From ANSYS Main Menu select Preprocessor → Modelling → Create → Vol-umes → Cylinder → By Dimensions. In response, a frame shown in Figure 7.56appears.


A cylinder created earlier (see Figure 7.52 for inputs) is reproduced (vol. 1).In order to create loading conditions at the contact interface, the cylinder is moved

toward the block by 0.05 units.From ANSYS Main Menu select Modelling → Move/Modify → Volumes. The

frame shown in Figure 7.57 appears.

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A


Selecting volume 1 and clicking [A] OK button calls up another frame shown inFigure 7.58.

B

A


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Figure 7.58 shows that the cylinder was moved by [A] 0.05 cm downward, i.e.,toward the block, after clicking [B] OK.

From Utility Menu select Plot → Replot to view the cylinder positioned inrequired location. Finally, from Utility Menu select PlotCtrls → View Settings →Viewing Direction. The frame shown in Figure 7.59 appears.

B

A

Figure 7.59 Viewing Direction.

By selecting [A] X, Y, and Z, coordinates as shown in Figure 7.59, clicking [B] OKbutton, and activating Plot → Replot command (Utility Menu), a half-symmetrymodel, shown in Figure 7.50, is finally created.

7.2.2.3 MATERIAL PROPERTIES

Before any analysis is attempted, it is necessary to define properties of the material tobe used.

From ANSYS Main Menu select Preferences. The frame in Figure 7.60 isproduced.

From the Preferences list [A] Structural option was selected as shown in Fig-ure 7.60. From ANSYS Main Menu select Preprocessor → Material Props →Material Models. Double click Structural → Linear → Elastic → Isotropic. Theframe shown in Figure 7.61 appears.

Enter [A] EX = 2.1 × 109 for Young’s modulus and [B] PRXY = 0.3 for Poisson’sratio. Then, click [C] OK and afterward Material: Exit. After defining propertiesof the material, the next step is to select element type appropriate for the analysisperformed. From ANSYS Main Menu select Preprocessor → Element Type →Add/Edit/Delete. The frame shown in Figure 7.62 appears.

Click [A] Add in order to pull down another frame, shown in Figure 7.63.In the left column click [A] Structural Solid and in the right column click [B]

Brick 8node 185. After that click [C] OK and Close in order to finish element typeselection.

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A

Figure 7.60 Preferences: Structural.

A

B

C


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A

Figure 7.62 Element Types.

B

C

A


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7.2.2.4 MESHING

From ANSYS Main Menu select Preprocessor → Meshing → MeshTool. The frameshown in Figure 7.64 appears.

There are a number of options available. First step is to go to Size Control: Linesoption and click [A] Set button. This opens another frame, as shown in Figure 7.65,prompting to pick lines on which element size is going to be controlled.

A

Figure 7.64 MeshTool options.

A

Figure 7.65 Element Size onPicked Lines.

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Pick two horizontal lines on the front edge of the cylinder and click [A] OK.The frame shown in Figure 7.66 appears.

A

B

C

Figure 7.66 Element Sizes on Picked Lines.

In the box [A] No. of element divisions type 3 and change selection [B] SIZE,NDIV can be changed to No. by checking the box and click [C] OK. Both selectionsare shown in Figure 7.66.

Similarly, using MeshTool frame, click Set button in the Size Controls → Linesoption and pick the curved line on the front of the block. Click OK afterward. Theframe shown in Figure 7.66 appears. In the box [A] No. of element divisions type 4this time and press [C] OK button.

In the frame MeshTool (see Figure 7.67) pull down [A] Volumes in theoption Mesh.

Check [B] Hex/Wedge and [C] Sweep options. This is shown in Figure 7.67.Pressing [D] Sweep button brings another frame asking to pick volumes to be

swept (see Figure 7.68).Pressing [A] Pick All button initiates meshing process. The model after meshing

looks like the image in Figure 7.69. Pressing [E] Close button in MeshTool frameends mesh generation stage.

After meshing completed, it is usually necessary to smooth element edges inorder to improve graphic display. It can be accomplished using PlotCtrls facility in

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A

B

C

D

E

Figure 7.67 Checked Hex and Sweep options.

A


the Utility Menu. From Utility Menu select PlotCtrls → Style → Size and Shape.The frame shown in Figure 7.70 appears.

In the option [A] Facets/element edge select 2 facets/edge and click [B] OKbutton to implement the selection as shown in Figure 7.70.

In solving the problem of contact between two elements, it is necessary to createcontact pair. Contact Wizard is the facility offered by ANSYS.

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A

B

Figure 7.70 Control of element edges.

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From ANSYS Main Menu select Preprocessor → Modelling → Create → ContactPair. As a result of this selection, a frame shown in Figure 7.71 appears.

A


Contact Wizard button is located in the upper left-hand corner of the frame.By clicking [A] on this button a Contact Wizard frame, as shown in Figure 7.72, isproduced.

B

A

C

Figure 7.72 Contact Wizard (target).

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A

Figure 7.73 Select body for Target.

In the frame shown in Figure 7.72 select[A] Body (volume), [B] Flexible, and press [C]Pick Target. The frame shown in Figure 7.73 isproduced.

Select block as target by picking on it andpress [A] OK button in the frame of Figure 7.73.Again Contact Wizard frame appears and thistime Next button should be pressed to obtain theframe shown in Figure 7.74.

Press [A] Pick Contact button to create theframe in Figure 7.75.

Pick cylinder as contact and press OK but-ton. Again Contact Wizard frame appears whereNext button should be clicked. The frame ofFigure 7.76 appears.

In this frame select [A] Coefficient of Fric-tion = 0.2 and check box [B] Include initialpenetration. Next press [C] Optional settingsbutton to call up another frame. In the new frame(Figure 7.77), Normal penalty stiffness = 0.1should be selected. Also, Friction tab located inthe top of the frame menu should be activatedand Stiffness matrix = Unsymmetric selected.

A

Figure 7.74 Contact Wizard (contact).

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A

Figure 7.75 Select Bodies for Contact.

Pressing [A] OK button brings back Contact Wizard frame (see Figure 7.76)where the [D] Create button should be pressed.

Created contact pair is shown in Figure 7.78.Finally, Contact Wizard frame should be closed by pressing Finish button. Also,

Contact Manager summary information frame should be closed.

7.2.2.6 SOLUTION

Before the solution process can be attempted, solution criteria have to be specified.As a first step in that process, symmetry constraints are applied on the half-symmetrymodel.

From ANSYS Main Menu select Solution → Define Loads → Apply → Struc-tural → Displacement → Symmetry BC → On Areas. The frame shown inFigure 7.79 appears.

Three horizontal surfaces should be selected by picking them and then clicking[A] OK. As a result, image shown in Figure 7.80 appears.

The next step is to apply constraints on the bottom surface of the block. FormANSYS Main Menu select Solution → Define Loads → Apply → Structural →Displacement → On Areas. The frame shown in Figure 7.81 appears.

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B

A

CD

Figure 7.76 Contact Wizard (optional settings).

After selecting required surface (bottom surface of the block) and pressing [A] OKbutton, another frame appears in which the following should be selected: DOFs to beconstrained = All DOF and Displacement value = 0. Selections are implemented bypressing OK button in the frame.

Because the cylinder has been moved toward the block by 0.05 cm, in order tocreate interference load, the analysis involves a large displacement effects.

From ANSYS Main Menu select Solution → Analysis Type → Sol’n Controls.The frame shown in Figure 7.82 appears.

In the pull down menu select [A] Large Displacement Static. Further selectedoptions should be: [B] Time at end of load step = 100; [C] Automatic time stepping(pull down menu) = Off; and [D] Number of substeps = 1. All specified selectionsare shown in Figure 7.82. Pressing [E] OK button implements the settings and closesthe frame.

Now the modeling stage is completed and the solution can be attempted. FromANSYS Main Menu select Solution → Solve → Current LS. A frame showing reviewof information pertaining to the planned solution action appears. After checking that

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A

Figure 7.77 Contact Properties (optional settings).

Figure 7.78 Contact Pair created by Contact Wizard.

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A

Figure 7.79 Apply SYMM on Areas.

Figure 7.80 Symmetry constraints applied on three horizontal areas.

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A

Figure 7.81 Apply U,ROT on Areas.

A

B

C

D

E


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everything is correct, select File → Close to close that frame. Pressing OK buttonstarts the solution. When the solution is completed, press Close button.

In order to return to the previous image of the model select Utility Menu → Plot→ Replot.

7.2.2.7 POSTPROCESSING

Solution results can be displayed in a variety of forms using postprocessing facility.For the results to be viewed for the full model, the half-symmetry model used foranalysis has to be expanded.

From Utility Menu select PlotCtrls → Style → Symmetry Expansion →Periodic/Cyclic Symmetry. Figure 7.83 shows the resulting frame.

A

B

Figure 7.83 Periodic/Cyclic Symmetry Expansion.

In the frame shown in Figure 7.83 [A] Reflect about XZ was selected. After clicking[B] OK button in the frame and selecting from Utility Menu, Plot → Elements, animage of full model, as shown in Figure 7.84, is produced.

The objective of the analysis presented here was to observe stresses in the cylinderproduced by the reduction of the initial gap between two blocks by 0.05 cm (aninterference fit). Therefore, form ANSYS Main Menu select General Postproc →Read Results → By Load Step. The frame shown in Figure 7.85 is produced.

The selection [A] Load step number = 1, shown in Figure 7.85, is implementedby clicking [B] OK button.

From ANSYS Main Menu select General Postproc → Plot Results → ContourPlot → Nodal Solu. In the resulting frame (see Figure 7.86) the following selectionsare made: [A] Item to be contoured = Stress and [B] Item to be contoured = vonMises (SEQV). Pressing [C] OK implements selections.

Contour plot of von Mises stress (nodal solution) is shown in Figure 7.87.

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Figure 7.84 Full model with mesh of elements and applied constraints.

A

B


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A

C

B


Figure 7.87 Contour plot of nodal solution (von Mises stress).

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Figure 7.87 shows von Mises stress contour for the whole assembly. If one is inter-ested in observing contact pressure on the cylinder alone then a different presentationof solution results is required.

A

B

C

D


From Utility Menu choose Select →Entities. The frame shown in Figure 7.88appears.

In the frame shown in Figure 7.88, thefollowing selections are made: [A] Elements(first pull down menu); [B] By Elem Name(second pull down menu); and [C] ElementName = 174. The element with the number174 was introduced automatically during theprocess of creation of contact pairs describedearlier. It is listed in the Preprocessor →Element Type → Add/Edit/Delete option.Selections are implemented by pressing [D]OK button.

From Utility Menu select Plot → Ele-ments. Image of the cylinder with mesh ofelements is produced (see Figure 7.89).

It is seen that the gap equal to 0.05 unitsexists between two half of the cylinder. Itis the result of moving half of the cylindertoward the block (by 0.05 cm) in order tocreate loading at the interface.

From ANSYS Main Menu select GeneralPostproc → Plot Results → Contour Plot →Nodal Solu. The frame shown in Figure 7.90appears.

In the frame shown in Figure 7.90, the following selections are made: [A] Contactand [B] Pressure. These are items to be contoured. Pressing [C] OK implementsselections made. In response to that an image of the cylinder with pressure contoursis produced as shown in Figure 7.91.

7.2.3 Wheel-on-rail line contact


Configuration of the contact to be analyzed is shown in Figure 7.92.This contact problem, which in practice is represented by a wheel-on-rail config-

uration, is well known in engineering. Also, the characteristic feature of the contactis that, nominally, contact between elements takes place along line. In reality, this isnever the case due to unavoidable elastic deformations and surface roughness. As aconsequence of that, surface contact is established between elements.

This is a 3D analysis and advantage could be taken of the inherent symmetry ofthe model. Therefore, the analysis will be carried out on a quarter-symmetry modelonly. The objective of the analysis is to observe the stresses in the cylinder and the railwhen an external load is imposed on them.

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Figure 7.89 Cylinder with surface elements (174).

A

B

C


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Figure 7.91 Contact pressure contours on the cylinder.

Figure 7.92 Configuration of the contact.

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The dimensions of the model are as follows: diameter of the cylinder = 1 cm andcylinder length = 2 cm. Rail dimensions: base width = 4 cm; head width = 2 cm; headthickness = 0.5 cm; and rail height = 2 cm.

Both elements are made of steel with Young’s modulus = 2.1 × 109 N/m2, Pois-son’s ratio = 0.3 and are assumed elastic. Friction coefficient at the interface betweencylinder and the rail is 0.1.

7.2.3.2 MODEL CONSTRUCTION

For the intended analysis a quarter-symmetry model is appropriate. It is shown inFigure 7.93.

The model is constructed using GUI facilities only. First, a two-dimensional(2D) model is created (using rectangles and circle as primitives). This is shown inFigure 7.94.

Next, using “extrude” facility, areas are converted into volumes and a 3D modelconstructed. When carrying out Boolean operations on areas or volumes, it is con-venient to have them numbered. This is done by selecting from the Utility Menu →

Figure 7.93 A quarter-symmetry model.

Figure 7.94 2D image(front) of the quarter sym-metry model. Involvedareas are numbered.

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PlotCtrls → Numbering and checking appropriate box to activate AREA (areanumbers) or VOLU (volume numbers) option.

From ANSYS Main Menu select Preprocessor → Modelling → Create →Areas → Rectangle → By Dimensions. The frame shown in Figure 7.95 appears.

A

B


Entered coordinates, [A] (X1 = 0; X2 = 2) and [B] (Y1 = −0.5; Y2 = −2.5), areshown in Figure 7.95. This creates area, A1.

From ANSYS Main Menu select Preprocessor → Modelling → Create →Areas → Rectangle → By Dimensions. Frame with entered coordinates, [A] (X1 = 1;X2 = 2) and [B] (Y1 = −0.5; Y2 = −1.5), is shown in Figure 7.96. This creates area, A2.

A

B


From ANSYS Main Menu select Preprocessor → Modelling → Create →Areas → Rectangle → By Dimensions. Frame with entered coordinates, [A](X1 = 0.5; X2 = 2) and [B] (Y1 = −1; Y2 = −1.5), is shown in Figure 7.97. Thiscreates area, A3.

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A

B


A

Figure 7.98 Subtract Areas.

From ANSYS Main Menu select Preproces-sor → Modelling → Operate → Booleans →Subtract → Areas. Frame shown in Figure 7.98appears asking for selection of areas to besubtracted.

Select first area, A1, by clicking on it. Thenclick [A] OK button in the frame of Figure 7.98.Next, select area A3, by clicking on it and pressing[A] OK button. Area A3 is subtracted from areaA1. This operation creates area, A4.

Repeat all the above steps in order to subtractarea A3 from area A4. As a result of this operation,a cross-section of half of the rail’s area is created.Its assigned number is A1.

Next, a quarter of a circle is created, which willbe extruded into a quarter of the cylinder. To dothat, it is necessary to offset WP (work plane) by90◦, so that the quarter circle will have a requiredorientation.

From Utility Menu select WorkPlane →Offset WP by Increments. Figure 7.99 shows theframe resulting from the selection.

It is seen from Figure 7.99 that ZX plane wasoffset by [A] 90◦ clockwise (clockwise direction isnegative).

From ANSYS Main Menu select Preprocessor→ Modelling → Create → Areas → Circle → By Dimensions. Frame shown inFigure 7.100 appears where appropriate data were entered to create a solid quarterof a circle with [A] outer radius of 0.5 cm, [B] starting angle 270◦, and [C] endingangle 360◦.

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A

Figure 7.99 Offset WP.

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A

B

C

Figure 7.100 Circular Area by Dimensions.

Figure 7.101 Isometric view of the 2D quarter model.

When the solid quarter circular area iscreated, it is important to restore WP offsetto its original setting. This can be done byfollowing steps associated with Figure 7.99and selecting XY, YZ, and ZX angles as 0, 0,and 90, respectively.

In an isometric view, the 2D quartermodel is shown in Figure 7.101.

It can be seen that the cross-section ofthe rail is assigned number A1 and the quar-ter of the solid circle is given number A2.

The next step is to extrude both areas,A1 and A2, into volumes.

From ANSYS Main Menu select Pre-processor → Modelling → Operate →Extrude → Areas → Along Normal. Theframe shown in Figure 7.102 appears.

Pick area A1 and click [A] OK but-ton to pull down another frame shown inFigure 7.103.

Selections made are shown in Fig-ure 7.103. By clicking [A] OK button, 2Dcross-section of the rail is extruded by [B]1 cm (length of extrusion) into a volume.

Direction of extrusion is normal to the rail’s cross-section.In a similar way, quarter solid circle can be extruded to create a quarter of the

cylinder with 1 cm length. Figure 7.104 shows the frame and selections made.

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A

Figure 7.102 Extrude Areas by Norm.

B

A

Figure 7.103 Extrude Area along Normal.

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A

Figure 7.104 Extrude Area along Normal.

It should be noted that in order to have the quarter cylinder oriented as required,[A] length of extrusion = −1 cm should be selected. The minus sign denotes directionof extrusion.

From Utility Menu select PlotCtrls → Numbering and check in VOLU and checkout AREA. This will change the system of numbering from areas to volumes. Rail isallocated number V1 and cylinder number V2. This completes the construction of aquarter-symmetry model, as shown in Figure 7.93.

7.2.3.3 PROPERTIES OF MATERIAL

Before any analysis is attempted, it is necessary to define properties of the material tobe used.

From ANSYS Main Menu select Preferences. The frame in Figure 7.105 isproduced.

As shown in Figure 7.105, [A] Structural was the option selected.From ANSYS Main Menu select Preprocessor → Material Props → Material

Models. Double click Structural → Linear → Elastic → Isotropic. The frame shownin Figure 7.106 appears.

Enter [A] EX = 2.1 × 109 for Young’s modulus and [B] PRXY = 0.3 for Poisson’sratio. Then click [C] OK button and afterward Material → Exit.

After defining properties of the material, the next step is to select element typeappropriate for the analysis performed.

From ANSYS Main Menu select Preprocessor → Element Type → Add/Edit/Delete. The frame shown in Figure 7.107 appears.

Click [A] Add in order to pull down another frame, as shown in Figure 7.108.In the left column click [A] Structural Solid and in the right column click [B]

Brick 8node 185. After that click [C] OK and Close in order to finish element-typeselection.

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A

Figure 7.105 Preferences: Structural.

A

B

C


7.2.3.4 MESHING

From ANSYS Main Menu select Preprocessor → Meshing → MeshTool. Then aframe shown in Figure 7.109 appears.

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A

Figure 7.107 Element types.

A

C

B


There are a number of options available. First step is to go to Size Control →Lines option and click [A] Set button. This opens another frame (shown in Figure7.110) prompting to pick lines on which element size is going to be controlled.

Pick two lines, one arcuate and the other horizontal in contact with the top surfaceof the rail, located on the front side of the cylinder and click [A] OK. The frame shownin Figure 7.111 appears.

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A

Figure 7.109 MeshTool.

In the box [A] No. of element divisions type 30 and change selection [B] SIZE,NDIV can be changed to No. by checking the box out and then click [C] OK. Bothselections are shown in Figure 7.111.

Similarly, using MeshTool frame (see Figure 7.109) click [A] Set in the SizeControls: Lines option and pick two lines located on top surface of the rail: onecoinciding with the line previously picked and the other at the right angle to the firstone. Click [A] OK as shown in Figure 7.110. The frame shown in Figure 7.111 appearsagain. In the box [A] No. of element divisions type 30 and press [C] OK button.

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A

Figure 7.110 Element Size on Picked Lines.

A

B

C

Figure 7.111 Element Sizes.

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A

B

C

D

Figure 7.112 MeshTool (checked Hex/Wedge and Sweep options).

A


In the frame MeshTool (see Figure 7.112) pull down [A] Volumes in the optionMesh. Check [B] Hex and [C] Sweep options.

Pressing [D] Sweep button brings another frame, as shown in Figure 7.113, askingto pick volumes to be swept.

Pressing [A] Pick All button initiates meshing process. The model after meshinglooks like the image in Figure 7.114.

Pressing Close button on MeshTool frame, ends mesh generation stage.

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After meshing being completed, it is usually necessary to smooth element edgesin order to improve graphic display. It can be accomplished using PlotCtrls facilityin the Utility Menu.

From Utility Menu select PlotCtrls → Style → Size and Shape. The frame shownin Figure 7.115 appears.

A

B

Figure 7.115 Size and Shape.

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In the option [A] Facets/element edge select 2 facets/edge and click [B] OKbutton as shown in Figure 7.115.


From ANSYS Main Menu select Preprocessor → Modelling → Create → ContactPair. As a result of this selection, a frame shown in Figure 7.116 appears.

A


Upper left-hand corner of the frame contains [A] Contact Wizard button. Byclicking on this button a Contact Wizard frame, as shown in Figure 7.117, is produced.

In the frame shown in Figure 7.117 select: [A] Areas, [B] Flexible, and press [C]Pick Target. The frame shown in Figure 7.118 is produced.

Select top area of the rail by picking on it and pressing [A] OK button in theframe of Figure 7.118. Again Contact Wizard frame appears and this time Nextbutton should be pressed to obtain the frame shown in Figure 7.119.

Press [A] Pick Contact button to create the frame in Figure 7.120.Select curved surface of the cylinder and press [A] OK button. Contact Wizard

frame appears again and Next button should be pressed to obtain the frame shownin Figure 7.121.

In the [A] Optional Settings frame select: set Coefficient of Friction = 0.1 andcheck out box – Include initial penetration. Next, press [A] Optional Settings buttonto call up another frame. In the new frame, Normal penalty stiffness = 0.1 should beselected. Also, Friction tab located in the top of the frame menu should be activatedand Stiffness matrix = Unsymmetric selected. Tab Initial Adjustment, also locatedat the top of the menu, should be pressed and in the box [A] Automatic ContactAdjustment selection Close gap should be made as shown in Figure 7.122.

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A B

C

Figure 7.117 Contact Wizard.

A

Figure 7.118 Select Areas for Target.

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A

Figure 7.119 Contact Wizard (contact).

A

Figure 7.120 Select Areas for Contact.

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